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  26 <div class="refentry">
  27 <a name="boost.accumulators.impl.immediate_rol_idp410515456"></a><div class="titlepage"></div>
  28 <div class="refnamediv">
  29 <h2><span class="refentrytitle">Struct template immediate_rolling_variance_impl</span></h2>
  30 <p>boost::accumulators::impl::immediate_rolling_variance_impl &#8212; Iterative calculation of the rolling variance. </p>
  31 </div>
  32 <h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
  33 <div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: &lt;<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.rolling_variance_hpp" title="Header &lt;boost/accumulators/statistics/rolling_variance.hpp&gt;">boost/accumulators/statistics/rolling_variance.hpp</a>&gt;
  34
  35 </span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Sample<span class="special">&gt;</span>
  36 <span class="keyword">struct</span> <a class="link" href="immediate_rol_idp410515456.html" title="Struct template immediate_rolling_variance_impl">immediate_rolling_variance_impl</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">accumulator_base</span> <span class="special">{</span>
  37   <span class="comment">// types</span>
  38   <span class="keyword">typedef</span> <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">fdiv</span><span class="special">&lt;</span> <span class="identifier">Sample</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">result_type</span> <a name="boost.accumulators.impl.immediate_rol_idp410515456.result_type"></a><span class="identifier">result_type</span><span class="special">;</span>
  39
  40   <span class="comment">// <a class="link" href="immediate_rol_idp410515456.html#boost.accumulators.impl.immediate_rol_idp410515456construct-copy-destruct">construct/copy/destruct</a></span>
  41   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <a class="link" href="immediate_rol_idp410515456.html#idp410560832-bb"><span class="identifier">immediate_rolling_variance_impl</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  42
  43   <span class="comment">// <a class="link" href="immediate_rol_idp410515456.html#idp410555072-bb">public member functions</a></span>
  44   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="immediate_rol_idp410515456.html#idp410555632-bb"><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  45   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="identifier">result_type</span> <a class="link" href="immediate_rol_idp410515456.html#idp410558016-bb"><span class="identifier">result</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  46
  47   <span class="comment">// <a class="link" href="immediate_rol_idp410515456.html#idp410562656-bb">private member functions</a></span>
  48   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
  49     <span class="keyword">void</span> <a class="link" href="immediate_rol_idp410515456.html#idp410563232-bb"><span class="identifier">prevent_underflow</span></a><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</span><span class="special">,</span>
  50                            <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">enable_if</span><span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span>
  51   <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
  52     <span class="keyword">void</span> <a class="link" href="immediate_rol_idp410515456.html#idp410566560-bb"><span class="identifier">prevent_underflow</span></a><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</span><span class="special">,</span>
  53                            <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">disable_if</span><span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span>
  54 <span class="special">}</span><span class="special">;</span></pre></div>
  55 <div class="refsect1">
  56 <a name="idp110700496"></a><h2>Description</h2>
  57 <p>Iterative calculation of sample variance <span class="inlinemediaobject"><img src="../../../images/accumulators//form_52.png"></span> is done as follows, see also <a href="http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance" target="_top">http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance</a>. For a rolling window of size <span class="inlinemediaobject"><img src="../../../images/accumulators//form_53.png"></span>, for the first <span class="inlinemediaobject"><img src="../../../images/accumulators//form_53.png"></span> samples, the variance is computed according to the formula </p>
  58 <div class="equation">
  59 <a name="idp110709168"></a><p class="title"><b>Equation&#160;1.9.&#160;</b></p>
  60 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_58.png" align="middle"></div></div>
  61 </div>
  62 <p><br class="equation-break"> where the sum of squares <span class="inlinemediaobject"><img src="../../../images/accumulators//form_59.png"></span> can be recursively computed as: </p>
  63 <div class="equation">
  64 <a name="idp110714464"></a><p class="title"><b>Equation&#160;1.10.&#160;</b></p>
  65 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_60.png" align="middle"></div></div>
  66 </div>
  67 <p><br class="equation-break"> and the estimate of the sample mean as: </p>
  68 <div class="equation">
  69 <a name="idp110717472"></a><p class="title"><b>Equation&#160;1.11.&#160;</b></p>
  70 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_61.png" align="middle"></div></div>
  71 </div>
  72 <p><br class="equation-break"> For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest sample <span class="inlinemediaobject"><img src="../../../images/accumulators//form_62.png"></span> is dropped from the window. The sample variance over the window now becomes: </p>
  73 <div class="equation">
  74 <a name="idp110723040"></a><p class="title"><b>Equation&#160;1.12.&#160;</b></p>
  75 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_63.png" align="middle"></div></div>
  76 </div>
  77 <p><br class="equation-break"> where the sum of squares <span class="inlinemediaobject"><img src="../../../images/accumulators//form_59.png"></span> now equals: </p>
  78 <div class="equation">
  79 <a name="idp110728448"></a><p class="title"><b>Equation&#160;1.13.&#160;</b></p>
  80 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_64.png" align="middle"></div></div>
  81 </div>
  82 <p><br class="equation-break"> and the estimated mean is: </p>
  83 <div class="equation">
  84 <a name="idp110731536"></a><p class="title"><b>Equation&#160;1.14.&#160;</b></p>
  85 <div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_65.png" align="middle"></div></div>
  86 </div>
  87 <p><br class="equation-break"></p>
  88 <p>Note that the sample variance is not defined for <span class="inlinemediaobject"><img src="../../../images/accumulators//form_66.png"></span>. </p>
  89 <div class="refsect2">
  90 <a name="idp110737056"></a><h3>
  91 <a name="boost.accumulators.impl.immediate_rol_idp410515456construct-copy-destruct"></a><code class="computeroutput">immediate_rolling_variance_impl</code>
  92         public
  93        construct/copy/destruct</h3>
  94 <div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <a name="idp410560832-bb"></a><span class="identifier">immediate_rolling_variance_impl</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span> args<span class="special">)</span><span class="special">;</span></pre></li></ol></div>
  95 </div>
  96 <div class="refsect2">
  97 <a name="idp110747744"></a><h3>
  98 <a name="idp410555072-bb"></a><code class="computeroutput">immediate_rolling_variance_impl</code> public member functions</h3>
  99 <div class="orderedlist"><ol class="orderedlist" type="1">
 100 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="keyword">void</span> <a name="idp410555632-bb"></a><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span> args<span class="special">)</span><span class="special">;</span></pre></li>
 101 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="identifier">result_type</span> <a name="idp410558016-bb"></a><span class="identifier">result</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span> args<span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li>
 102 </ol></div>
 103 </div>
 104 <div class="refsect2">
 105 <a name="idp110769616"></a><h3>
 106 <a name="idp410562656-bb"></a><code class="computeroutput">immediate_rolling_variance_impl</code> private member functions</h3>
 107 <div class="orderedlist"><ol class="orderedlist" type="1">
 108 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
 109   <span class="keyword">void</span> <a name="idp410563232-bb"></a><span class="identifier">prevent_underflow</span><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</span> non_negative_number<span class="special">,</span>
 110                          <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">enable_if</span><span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span></pre></li>
 111 <li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
 112   <span class="keyword">void</span> <a name="idp410566560-bb"></a><span class="identifier">prevent_underflow</span><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</span> non_arithmetic_quantity<span class="special">,</span>
 113                          <span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">disable_if</span><span class="special">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span></pre></li>
 114 </ol></div>
 115 </div>
 116 </div>
 117 </div>
 118 <table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
 119 <td align="left"></td>
 120 <td align="right"><div class="copyright-footer">Copyright &#169; 2005, 2006 Eric Niebler<p>
 121         Distributed under the Boost Software License, Version 1.0. (See accompanying
 122         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
 123       </p>
 124 </div></td>
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